Considering the individual constraints of adaptive and robust control, recently global research is reoriented towards adaptive-robust control (ARC). The series of publications [1]}, [2]}-[3]} regarding ARC, estimate the individual uncertain system parameters through adaptive law and robust control is utilized to negate the effect of external disturbances. These works utilize the projection operator in their respective adaptive laws which necessitate the knowledge of lower and upper bound of individual uncertain system parameters. Adaptive sliding mode control (ASMC) is designed in [4]} for parameter identification of mechanical servo systems with LuGre friction considering the uncertainties to be linear in parameters (LIP). In contrast, the controllers [5]}-[6]} assume that the overall uncertainty (or its time derivative) is bounded by some constant. Thereafter, that constant term is estimated by adaptive law, rather estimating individual uncertain system parameters. The adaptive laws in [7]}-[8]} involve a predefined threshold value; as a matter of fact, until the threshold value is achieved, the switching gain may still be increasing (resp. decreasing) even if the tracking error decreases (resp. increases) and thus creates overestimation (resp. underestimation) problem of switching gain.While the underestimation problem compromises the controller accuracy by applying lower switching gain than the required amount, the overestimation problem causes larger gain and high control input requirement.
The adaptive law reported in [9]} requires predefined bound on the time derivative of the uncertainties. As observed in [6]}, the method in [9]} also requires frequency characteristics of the perturbation to design the filter for equivalent control. However, the work in [6]} assumed that the time derivative of the uncertainties are bounded by an unknown constant.
